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The velocity of an object at time $t$ traveling in a straight line along the $x$-axis is given by:

$$v(t)=2t^{3}-17t^{2}+38t-15$$

If the initial position of the object is $x(0)=5$, find the total distance traveled by the particle during the time $0\leq t\leq 5$.

A

$4.167$

B

$9.167$

C

$29.688$

D

$34.688$

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